Fractal Metrology for biogeosystems analysis (original) (raw)
Related papers
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes. In the present research, this pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay) and compared in terms of 5 roughness of the gray-intensity distribution (the measurand) quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them and to the measurement function which best fits to the experimental results. Some of the applied techniques are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently de-10 veloped by our Group. The combination of all these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM through a case study of soil physical and chemical degradation applying the selected toolbox to describe and compare the main structural attributes of three porous media with contrasting structure 15 but similar clay mineralogy dominated by montmorillonites.
Fractal approach in characterization of spatial pattern of soil properties
EURASIAN JOURNAL OF SOIL SCIENCE (EJSS), 2017
The objective of the study was to characterize spatial pattern of soil properties (CaCO3, soil organic carbon, P2O5, K2O, and clay content) using fractal concept. Total of 141 topsoil samples (0-30 cm) were collected on 1850 ha in karst polje (Petrovo polje, Croatia) and analyzed for listed soil properties. The semi-variogram method was used to estimate fractal dimension (D) value which was performed from both of isotropic and anisotropic perspective. The D value of soil properties ranged between 1.76 to 1.97, showing a domination of the short-range variations. The SOC and K2O fractal D values 1.79 and 1.76 respectively, exhibited a spatial continuity at the entire analysed range of the scale. The D value for P2O5 (1.97) showed a nearly total absence of the spatial structure at all scales. The CaCO3 and clay content indicated a multifractal behavior mainly attributed to effects of alluviation, differences in geology and its spatial changes and transitions. The results of anisotropic analysis of soil properties pattern have showed strong relations with directions and partial self-similarity over limited ranges of scales defined by scale-break. Finally, our results showed that fractal analysis can be used as a appropriate tool for the characterization of spatial pattern irregularities of soil properties and detection of soil forming factors that cause it.
Fractal geometry applied to soil and related hierarchical systems
Geoderma, 2006
Fractal geometry applied to soil and related hierarchical systems Complexity is an intrinsic quality of soil and related hierarchical Earth materials such as saprolite, rock, and marine sediments. It is the product of manifold feedbacks and multiscale interactions, which generate spatial and temporal heterogeneities in the properties and dynamics of natural porous media. Such heterogeneities can create substantial difficulties in environmental research since no experimental sample, site, or procedure is sufficient to fully represent the biogeochemical complexity that is present in the natural medium under study. Because geometric measurements are at the heart of any research, the correct and efficient characterization of complex systems presents both a challenge and a necessity. Any measurement is based on some underlying model representation of the system in question. Fractal geometry has long been advocated as a better representation of complex particulate media as compared with simple Euclidean models based on straight lines and circle arcs. Recent developments in this field, including the application of information theory and multifractals to characterize natural hierarchical systems, were explored at the 6th International Workshop on "Fractal Mathematics Applied to Soil and Related Heterogeneous Systems" (PEDOFRACT 2004), which took
Linear fractal analysis of three Mexican soils in different management systems
Soil Technology, 1997
The purpose of this study was to document the fractal nature of three soils of Mexico with contrasting genesis and marked differences in morphology and to estimate the fractal dimensions of their sets of aggregates and pores. These dimensions were estimated along lines and were called linear fractal dimensions. A single, 'ideal' fractal dimensionality was detected in the three soils studied. The soil linear fractal dimensions, calculated from macro and micromorphological data, had larger values than the dimension of the Cantor fractal dust model, but were less than unity. It was shown, that the fractal structure of the soil pore space could not be described by the same dimension as that of the aggregates. The linear fractal dimensions of soils of distinct genesis, were significantly different on all scales compared, but the differences fluctuated between 0.4% and 9.1%. 0 1997 Elsevier Science B.V.
Fractal and compositional analysis of soil aggregation
A soil aggregate is made of closely packed sand, silt, clay, and organic particles building up soil structure. Soil aggregation is a soil quality index integrating the chemical, physical, and biological processes involved in the genesis of soil structure and tilth. Aggregate size distribution is determined by sieving a fixed amount of soil mass under mechanical stress and is commonly synthesized by the mean weight diameter (MWD) and fractal dimensions such as the fragmentation fractal dimensions ( ). A fractal is a rough object that can be broken down into a number of reduced-size copies of the original object. Equations have been developed to compute bounded and unbounded scaling factors as measures of fractal dimensions based on assumptions about average diameter, bulk density, shape and probability of failure of sieved particles. The log-log relationship between particle diameter and cumulative number or mass of aggregates or soil particles above a given diameter often shows more or less uniform fractal patterns. Multi-fractal (slopes showing several values ≤ 3) and non fractal patterns or incomplete fragmentation ( ) have been reported. Scaling factors are curvefitting parameters that are very sensitive to the choice of the fractal domain about breakpoints. Compositional data analysis using sequential binary partitions for isometric log ratio (ilr) coordinates with orthonormal basis provides a novel approach that avoids the assumptions and dimensional constraints of fractal analysis. Our objective was to compare MWD, fractal scaling factors and ilr coordinates using published data. In the first dataset, MWD was found to be biased by excessively high weight being given to the largest aggregate-size. Eight ilr coordinates contrasting micro-vs. macro-aggregates were related to fragmentation fractal dimensions, most of which were below 2 or above 3, a theoretical impossibility for geometric fractals. The critical ilr value separating scaling factors 3 and > 3 was close to zero. In a second dataset, the Aitchison distance computed across ilr coordinates proved to be a useful measure of the degree of soil aggregation, agradation or degradation against a reference composition such as that of primary particles, bare fallow or permanent grass. The individual contributions of ilr coordinates to the Aitchison distance can be interpreted in terms of sign and amplitude and be related to soil properties and processes mediated by soil aggregation.
Application of fractal analysis in agriculture
The purpose of this review was to present and discuss methods and indices used to characterize soil structure and texture by means of fractal analysis. The method of determination of fractal dimension based on Sierpinski carpet model and the box counting is described. A planar soil samples of the loam clay soil are evaluated by method of image analysis and surface fractal dimension of solid partitions and pores are determined.
The fractal dimension of pore distribution patterns in variously-compacted soil
Soil and Tillage Research, 1998
Pore-size distribution pattern signi®cantly alters many soil properties affecting water movement and root growth. The distribution is largely in¯uenced by soil compaction but information on how to describe this effect is very limited. In this study we used the fractal dimension to characterize pore distribution patterns in variously-compacted soil. The soil used was an Orthic Luvisol (Lublin Region, Poland). The various soil compaction was obtained by wheel traf®c treatments: unwheeled (L); moderately compacted, 3 tractor passes (MC); strongly compacted, 8 tractor passes (SC). Pore distribution patterns of all pores (>0.3 mm) and water-conducting pores were analyzed with an image analyzer and the two-dimensional fractal dimension was estimated. All pores were analyzed on the drawings obtained from the polished surfaces of soil blocks 8Â9Â2 cm. To analyze the water-conducting pores, soil cores were taken in cylinders of length 20 cm and diameter 21.5 cm from the plots on which methylene blue solution was applied. The pores were analyzed on horizontal cuts at 2 cm depth intervals. Mean values of fractal dimensions for all pores (D p 2) in the horizontal plane of surface soil in L, MC and SC were 1.69, 1.42 and 1.35, respectively. In the vertical plane, the corresponding values were 1.48, 1.35 and 1.29. In L the fractal dimension re¯ected pores of different size ranging from a few tenths of a millimetre to a dozen or so millimetres with rather smooth walls. In MC the contribution of large pores decreased whereas that of medium-sized pores considerably increased forming net-like patterns. However in SC, the largest area was of massive structure with longitudinal cracks and scarce and unevenly-distributed larger pores. The D p 2 was linearly correlated with areal porosity (R0.965) and the arithmetic mean of the areas of pores (R0.914). Mean values of fractal dimensions for the blue staining patterns (D s 2) in the plough layer ranged from 1.06 to 1.12 in L and MC whereas it decreased to 0.94 in SC. The wide range of D s 2 values for 2 cm layers of upper soil in L re¯ected the high variability of pore structures in this treatment. In the subsoil, the D s 2 varied from 1.03 to 1.09 and re¯ected mostly the distribution pattern of earthworm channels. The values of fractal dimensions for roots (D r 2) re¯ected different branching and root growth in variously-compacted soil. This study showed that fractal analysis provides a relevant quanti®cation of the changes of pore and root structure in relation to soil compaction. #
2016
Fractal geometry and geostatistics have become effective tools for quantifying spatial variability of soil physical. In this research, fractal dimension (Dm) of Particle Size Distribution (PSD) was used to explain relationships between Dm and some physical properties of soils. Samples from 51 soil series with varying properties were collected from north of Iran. Sand fraction was determined by sieving and silt and clay fractions by the hydrometer methods. Fractal dimension of PSD was computed by Tyler & Wheatcraft model. Statistical analysis showed significant and positive correlations between Dm and clay (0.93) and silt (0.80) particles; and the correlation between Dm and sand (0.73) were significantly negative. Therefore, Dm had significant relations with soil textural fractions and textural classes, and might be used as an integrating index in modeling studies. Results also showed that greater Dm was associated with greater self-similarity in pore size distribution.
Fractal analysis of microstructure of peat soil
This study discusses fractal analysis on the microscopic structure of the peat soil. The main objective is to investigate the distribution of pores in the rock samples. The results of fractal analysis using the Minkowski-Bouligand method indicates that the SEM images of microscopic structures of peat soil behave as a fractal with dimension value 1.8965. These values confirm that the distribution of pores in the peat soil is very irregular at the microscale levels.
Evaluation of Soil-Water Characteristic Curves for Different Textural Soils Using Fractal Analysis
Water
The soil-water characteristic curve (SWCC) is an essential tool to determine hydraulic and mechanical properties of unsaturated soils. As an inherent influencing factor, soil texture controls the characteristics of SWCCs. Fractal theory can quantitatively describe the physical characteristics of soil. This study used particle size distribution data and water content data contained in the UNSODA2.0 database to explore the fractal characteristics of 12 soil types with different textures under different matrix suctions. The SWCC fractal model was adopted to characterize the hydraulic properties of soil with various soil textures. The findings revealed that the mass fractal dimensions of particles from these 12 different soil types significantly differed and were closely related to the clay content. Fractal dimension increased with increasing clay content. The fractal dimension established a good relationship between soil structure and hydraulic properties. Fractal analysis can be used ...